Question

2 identify the extrema: relative minimum: (0,0) absolute minimum: (3, - 4) relative minimum: (3, - 4) absolute maximum: (1, 1) relative maximum: (1, 1) absolute minimum: (0,0)

Explanation:

Step1: Define relative and absolute extrema

Relative extrema are local maximum or minimum points. Absolute extrema are the overall maximum or minimum points on the entire domain shown.

Step2: Identify relative maximum

The point $(1,1)$ is a relative maximum as the function changes from increasing to decreasing at that point.

Step3: Identify relative minimum

The point $(3, - 4)$ is a relative minimum as the function changes from decreasing to increasing at that point.

Step4: Identify absolute minimum

Among all the points on the graph, the point $(3,-4)$ has the lowest $y$-value, so it is the absolute minimum.

Answer:

Relative minimum: $(3, - 4)$
Absolute minimum: $(3, - 4)$
Relative maximum: $(1,1)$